Group Theoretical Approach to the Coherent and the Squeeze States of a Time-Dependent Harmonic Oscillator with a Singular Term

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dc.creatorKim, Jung Kon
dc.creatorKim, Sang Pyo
dc.date1995-11-13
dc.date.accessioned2026-07-07T06:13:39Z
dc.date.available2026-07-07T06:13:39Z
dc.descriptionFor a time-dependent harmonic oscillator with an inverse squared singular term, we find the generalized invariant using the Lie algebra of $SU(2)$ and construct the number-type eigenstates and the coherent states using the spectrum-generating Lie algebra of $SU(1,1)$. We obtain the evolution operator in both of the Lie algebras. The number-type eigenstates and the coherent states are constructed group-theoretically for both the time-independent and the time-dependent harmonic oscillators with the singular term. It is shown that the squeeze operator transforms unitarily the time-dependent basis of the spectrum-generating Lie algebra of $SU(1,1)$ for the generalized invariant, and thereby evolves the initial vacuum into a final coherent vacuum.
dc.description22 pages of Latex file
dc.identifierhttps://arxiv.org/abs/quant-ph/9511013
dc.identifierhttp://arxiv.org/abs/quant-ph/9511013
dc.identifierJ.Korean Phys.Soc. 28 (1995) 7
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/93183
dc.subjectQuantum Physics
dc.titleGroup Theoretical Approach to the Coherent and the Squeeze States of a Time-Dependent Harmonic Oscillator with a Singular Term
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